The sum of two consecutive integers is 129. Find both integers.
I will assume consecutive to mean that the integers have a difference between them of 1.
We can now define 2 integers, a and b, and say that a > b.
From this we know that, given the difference is equal to one: a + 1 = b.
We also know that a + b = 129.
Substituting the alternative form of b in, we have: a + (a + 1) = 129.
After combining terms (grouping), we have: 2a + 1 = 129.
After isolating variables (getting a alone on one side), we get 2a = 128, which, when dividing each side, resolves into a = 64.
Plugging a back into the above equation, we find b = (64) + 1, or b = 65.
The consecutive integers are therefore 64 and 65.